If $${\text{ }}x - \sqrt 3 - \sqrt 2 = 0$$ and $$y - \sqrt 3 + \sqrt 2 {\text{,}}$$ then the value of $$\left( {{x^3} - 20\sqrt 2 } \right) - $$ $$\left( {{y^3} + 2\sqrt 2 } \right)?$$
A. 2
B. 3
C. 1
D. 0
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{According to the question,}} \cr & x = \sqrt 3 + \sqrt 2 \cr & y = \sqrt 3 - \sqrt 2 \cr & \left( {{x^3} - 20\sqrt 2 } \right) - \left( {{y^3} + 2\sqrt 2 } \right) \cr & = \left[ {{{\left( {\sqrt 3 + \sqrt 2 } \right)}^3} - 20\sqrt 2 - {{\left( {\sqrt 3 - \sqrt 2 } \right)}^3} - 2\sqrt 2 } \right] \cr} $$$$ = 3\sqrt 3 + 2\sqrt 2 + 9\sqrt 2 + 6\sqrt 3 \, - $$ $$20\sqrt 2 \, - $$ $$3\sqrt 3 \,\, + $$ $$2\sqrt 2\,\, + $$ $$9\sqrt 2 \, - $$ $$6\sqrt 3\, - $$ $$2\sqrt 2 $$
$$\eqalign{ & = 9\sqrt 3 - 9\sqrt 2 - 9\sqrt 3 + 9\sqrt 2 \cr & = 0 \cr} $$
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